TBR Physics Chapter 1

[MedPR]

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So I'm trying to figure out how to derive this equation and I'm completely baffled. I'm sure there's something very simple that I'm missing, but could someone please help me out.

It's equation 1.27 on page 29 (2012 book). The equation is h = (vo^2)/2g

I know that h = vot + 1/2a(t^2) but I can't figure out where the above equation comes from.

Thanks.

-------------Edit--------------

Nevermind, figured it out. I forgot that t=vo/g. If anyone else was wondering the same thing, here's what you do.

Using:
h=vot - 1/2g(t^2)
t=vo/g

Rewrite as h= (vo - 1/2gt) * t

Substitute for t:

h= (vo - 1/2g*vo/g) * vo/g

Multiply through:

h= (vo^2/g - 1/2g*vo^2/g^2)

Simplify:

h= vo^2/g - 1/2*vo^2/g

To subtract you need a common denominator of 2.

h = 2vo^2/2g - vo^2 / 2g

h=vo^2/2g

 

[Erythropoietin]

Yea watch out for the x vs y components for that formula.

 

[MedPR]

Yea watch out for the x vs y components for that formula.

Yea, what I have is all y components though, right? h=vo^2/g is always only going to have a y component.

 

[study pray love]

simple energy conservation: mgh=1/2mv^2
when you cancel the masses and divide 1/2 v^2/g you get v^2/2g=h

 

[MedPR]

simple energy conservation: mgh=1/2mv^2
when you cancel the masses and divide 1/2 v^2/g you get v^2/2g=h

MIND BLOWN! Thanks, that will help me memorize and understand.

 

[study pray love]

happy to help=)

 

[Erythropoietin]

Yea, what I have is all y components though, right? h=vo^2/g is always only going to have a y component.

yes that's all y components when you set the initial velocity in the y-direction to be zero

 

[lulume]

Thanks for the answer!